Question

An electric pole was knocked over and is leaning at a 104 degree angle due to a recent storm. As a result, the power lines are hanging too low so some electricians were sent out to look in to the situation. One electrician is sitting 36 meters away from the base of the pole (on the obtuse angle side).

Although it is too dangerous to measure the length of the pole directly, the electricians can measure the angle of elevation from the ground to the top of the pole and then calculate the length based off of that. If the angle of elevation from the electrician to the top of the pole is 33.6 degrees, what is the length of the pole?

Round your answer to the nearest hundredth of a meter.

Answer 1

29.54 m

Explanation:

You want the side opposite the 33.6° angle in a triangle that is 36 m between its 33.6° angle and its 104° angle.

Law of sines

In order to use the law of sines to find an unknown side opposite a given angle, we must have a known angle opposite a known side. The known side is opposite the third angle of the triangle, whose measure is ...

180° -104° -33.6° = 42.4°

Now, we can use the law of sines:

pole height/sin(33.6°) = (36 m)/sin(42.4°)

pole height = (36 m)·sin(33.6°)/sin(42.4°) ≈ 29.54475 m

pole height ≈ 29.54 m